Passive inter-modulation distortion (“PID”) is a form of electrical interference that may occur when two or more RF signals encounter non-linear electrical junctions or materials along an RF transmission path. Such non-linearities may act like a mixer causing the RF signals to generate new RF signals at mathematical combinations of the original RF signals. These newly generated RF signals are referred to as “inter-modulation products.” The newly generated RF signals fall within the bandwidth of existing RF signals. This may occur, for example, when signals transmitted through a device generate inter-modulation products that fall in the same bandwidth of signals that are received through the same device. If this occurs, the noise level experienced by the existing RF signals in the receiver bandwidth is increased. When the noise level is increased, it may be necessary to reduce the data rate and/or the quality of service. PID can be an important interconnection quality characteristic, as PID generated by a single low quality interconnection may degrade the electrical performance of the entire RF communications system. Thus, ensuring that components used in RF communications systems will generate acceptably low levels of PID may be desirable.
The above-described inter-modulation products arise because non-linear systems generate harmonics in response to sinusoidal inputs. For example, when a signal having a first frequency Sf1 is input to a non-linear system, then the resulting output signal will include signals at integer multiples of the input frequency. When two or more signals having different frequencies are input to a non-linear system, inter-modulation products arise. For example, consider a composite input signal x(t) to a non-linear system that includes signals at three different frequencies:x(t)=A1 sin(2πf1t+φ1)+A2 sin(2πf2t+φ2)+A3 sin(2πf3t+φ3)  (1)
In Equation (1) above, Ai and φi are the amplitudes and phases of the signals at the three different frequencies f1, f2, f3. These signals are passed through a non-linearity. The resulting output signal will include components at the frequencies f1, f2, f3 of the three input signals, which are referred to as the fundamental components, as well as linear combinations of these fundamental components having the form:k1f1+k2f2+k3f3  (2)
where k1, k2, k3 are arbitrary integers which can have positive or negative values. These components are the inter-modulation products and harmonics, and will have amplitudes and phases that are a function of the non-linearity and the composite input signal x(t).
The order of an inter-modulation product is the sum of the absolute value of the coefficients 1c, included in the inter-modulation product. In the above example where the composite input signal x(t) includes signals at three different frequencies, the third order inter-modulation products are the inter-modulation products where:|k1|+|k2|+|k3|=3, where |k1|,|k2|,|k3|<3  (3)
In the above example, the third-order inter-modulation products will be at the following frequencies:f1+f2−f3 f1+f3−f2 f2+f3−f1 2f1−f2 2f1−f3 2f2−f1 2f2−f3 2f3−f1 2f3−f2 
The odd-order inter-modulation products are typically of the most interest as these products are the ones that tend to fall in the vicinity of the frequencies of the fundamental components.
PID may be caused by, for example, inconsistent metal-to-metal contacts along an RF transmission path, particularly when such inconsistent contacts are in high current density regions of the transmission path such as inside RF transmission lines, inside RF components, or on current carrying surfaces of an antenna. Such inconsistent metal-to-metal contacts may occur, for example, because of contaminated and/or oxidized signal carrying surfaces, loose connections between two connectors, metal flakes or shavings inside RF components or connections and/or poorly prepared soldered connections (e.g., a poor solder termination of a coaxial cable onto a printed circuit board). PID may arise in a variety of different components of an RF communications system. For example, non-linearities may exist at the interconnections in an RF communications system where cables such as coaxial cables are connected to each other or to RF equipment. PID may also arise in other components of an RF communications system such as RF amplifiers, duplexers, cross-band couplers, interference mitigation filters and the like. PID may also arise on or within radiating elements of the RF communications system such as parabolic antennas or phased array antenna elements. The non-linearities that give rise to PID may be introduced at the time of manufacture, during installation, or due to electro-mechanical shift over time due to, for example, mechanical stress, vibration, thermal cycling, and/or material degradation.
PID testing is routinely performed to identify components and/or interconnections that exhibit unacceptably high levels of PID. International standard IEC 62037 sets out acceptable techniques for measuring PID. Typically, various components of an RF transmission system will be rated to have PID levels below certain ranges when tested according to the above-referenced international standard. PID measurements may specify, for example, a magnitude of a third order inter-modulation distortion signal.